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Re: [Phys-l] relativity misconception #437



On 10/12/2011 07:45 AM, Bill Nettles wrote:
JD said:" What we care about is the coordinate system. Moe himself
is moving toward the future at the rate of 60 minutes per hour, in
accordance with answer (B), but his coordinate system is not. In
particular the contours of constant time in his coordinate system are
not moving, and those are what we normally use to measure spacetime
positions, velocities, et cetera."

Does this mean that there are continually "new" coordinate systems
that are instantaneous with Moe,

That cuts right to the core of the issue.

I don't know of any good way to answer that question, except by
slightly reframing the discussion, so that I get to answer a
slightly different question.

See if you can go along with me on this: In high school algebra,
when you learned about polar coordinate systems and rectangular
coordinate systems, you didn't need to antropomorphize them.
You didn't need an "observer" attached to each coordinate system.

From there it is just a small step to set up coordinate systems
in spacetime ... without the "observer". Just think of it as
the /red/ coordinate system.

Once you've got a well-behaved coordinate system, we can use it
to describe what happens to Moe. He moves along his worldline,
getting older. What happens to Moe does not affect the red
coordinate system. The coordinate system does not "belong" to
Moe.

A stopwatch (unlike an ordinary clock) can easily be reset to
zero. In this way you could -- if you wanted -- set up a whole
series of different coordinate systems, each with a different
origin. Sometimes that's helpful, you don't want to do toooo
much of it, because comparing observations in one frame to
observations in another frame creates extra work.

In the introductory class, I recommend setting up a red coordinate
system and leaving it at that. If you want to talk about Moe,
let him sit at [t, x, y, z] where x, y, and z are constant but
t is not constant. Moe is at rest in the sense that his 3-velocity
is zero, but his 4-velocity is [1, 0, 0, 0].

Failure to clearly distinguish 3-velocity from 4-velocity is
yet another misconception.

I've always thought of Moe actually BEING the coordinate system

Again: I'm recommending against that. We don't do that with
polar coordinates, and we shouldn't do it with Minkowski coordinates.

If we are to have any hope of talking about the age of Moe, we
have to measure that against something else ... against some
contours of constant time ... against a reference frame. If you
ask Moe what time it is, and he says "the time is NOW" that's
not very helpful.

If Moe is anything like a real person, he *must* move past the
coordinate system at a rate of 60 minutes per hour. If you
still aren't happy with that, imagine a /clock/ moving past
the coordinate system, moving past the contours of constant time.

Here's a figure in the red reference frame:
http://www.av8n.com/physics/spacetime-welcome.htm#fig-ruler-cart-t-const-x-red:s
and the companion figure in the blue reference frame:
http://www.av8n.com/physics/spacetime-welcome.htm#fig-ruler-cart-t-const-x-blue:s

Note: The document:
http://www.av8n.com/physics/spacetime-welcome.htm

is only about half finished. You can read it if you want.
Comments are always welcome ... but comments of the form
"section 2.9 is missing" are not necessary at this point.

The plan is to heavily emphasize the geometry and trigonometry
of spacetime, using lots of pictures.

Also the plan is to put the big ideas out early, and to put
some real-world applications out early ... rather than starting
from some axioms and deriving everything step by step. This
is not high-school geometry, where I am obliged to prove each
idea before using it. I reckon that /after/ the big ideas are
out there, we will have plenty of time (and better motivation)
to delve into the details. The details guarantee consistency
of the picture ... but the picture is plausible without them.

For folks who like the step-by-step axiomatic derivation
approach, there's lots of that in the literature already.